Preliminary report with traditional stability, Effect of climatic extremes on community stability and its drivers
Shyamolina Ghosh, Owen Petchey
25 October, 2023
1 Introduction
2 Data
2.1 Data structure
Total 1947 community timeseries we have collected for the timespan 1979-2019. 4 taxa are considered - birds, fish, freshwater invertebrates, terrestrial invertebrates. Below is the summary of the datatable. Description of each column is given in README.txt
## 'data.frame': 1947 obs. of 55 variables:
## $ source : chr "BioTIME" "BioTIME" "BioTIME" "BioTIME" ...
## $ STUDY_ID : chr "57" "229" "229" "229" ...
## $ newsite : chr "57" "STUDY_ID_229_LAT35.04016_LON-83.36127" "STUDY_ID_229_LAT35.11187_LON-83.39091" "STUDY_ID_229_LAT35.14137_LON-83.29577" ...
## $ REALM : chr "Freshwater" "Freshwater" "Freshwater" "Freshwater" ...
## $ TAXA : chr "fish" "fish" "fish" "fish" ...
## $ ORGANISMS : chr "fish" "fish" "fish" "fish" ...
## $ initR : int 76 24 30 32 25 37 22 30 26 31 ...
## $ nsp : int 34 14 11 17 14 16 13 11 14 10 ...
## $ nyr_used : int 32 23 20 21 21 23 23 20 20 28 ...
## $ startyr : int 1981 1990 1990 1991 1990 1990 1990 1995 1995 1979 ...
## $ endyr : int 2012 2013 2013 2012 2013 2013 2013 2014 2014 2006 ...
## $ nint : int 561 91 55 136 91 120 78 55 91 45 ...
## $ nind : int 503 59 35 97 61 91 67 46 60 36 ...
## $ npos : int 35 29 20 27 29 27 11 7 26 7 ...
## $ nL : int 24 21 13 9 3 14 3 3 15 7 ...
## $ nU : int 11 8 7 18 26 13 8 4 11 0 ...
## $ nneg : int 23 3 0 12 1 2 0 2 5 2 ...
## $ L : num 3.027 2.557 1.046 1.028 0.267 ...
## $ U : num -1.252 -0.633 -0.49 -2.547 -2.938 ...
## $ f_nind : num 0.897 0.648 0.636 0.713 0.67 ...
## $ f_nL : num 0.0428 0.2308 0.2364 0.0662 0.033 ...
## $ f_nU : num 0.0196 0.0879 0.1273 0.1324 0.2857 ...
## $ f_nneg : num 0.041 0.033 0 0.0882 0.011 ...
## $ cvsq_real : num 1.565 0.189 0.239 0.11 0.158 ...
## $ cvsq_indep : num 1.5001 0.0963 0.0879 0.0475 0.1099 ...
## $ phi : num 1.04 1.96 2.72 2.33 1.44 ...
## $ phi_LdM : num 0.454 0.552 0.388 0.442 0.542 ...
## $ skw_real : num 5.172 0.363 0.505 2.41 -0.296 ...
## $ skw_indep : num 5.064 0.612 0.737 0.841 -0.877 ...
## $ phi_skw : num 1.021 0.593 0.685 2.866 0.337 ...
## $ iCV : num 0.799 2.303 2.045 3.008 2.512 ...
## $ iCValt : num 1.81 1.9 1.56 3.7 2.15 ...
## $ LONGITUDE : num -89.5 -83.4 -83.4 -83.3 -83.5 ...
## $ LATITUDE : num 44 35 35.1 35.1 35.2 ...
## $ t_med : num 2809 2865 2868 2864 2864 ...
## $ t_skw : num 0.4702 0.1315 0.1711 -0.0306 0.0381 ...
## $ t_var : num 0.00401 0.00228 0.00208 0.00233 0.00239 ...
## $ t_med_celcius : num 7.77 13.31 13.67 13.23 13.2 ...
## $ t_skw_celcius : num 0.4702 0.1315 0.1711 -0.0306 0.0381 ...
## $ t_var_celcius : num 0.145 0.0492 0.0438 0.0504 0.0518 ...
## $ t.lm.slope : num 0.341 0.258 0.106 0.365 0.2 ...
## $ t.lm.slope.sig : int 1 0 0 0 0 0 0 0 0 0 ...
## $ t.sens.slope : num 0.333 0.333 0.215 0.448 0.319 ...
## $ t.sens.slope.sig : int 0 0 0 0 0 0 0 0 0 0 ...
## $ t.lm.slope.celcius : num 0.0341 0.0258 0.0106 0.0365 0.02 ...
## $ t.lm.slope.sig.celcius : int 1 0 0 0 0 0 0 0 0 0 ...
## $ t.sens.slope.celcius : num 0.0333 0.0333 0.0215 0.0448 0.0319 ...
## $ t.sens.slope.sig.celcius: int 0 0 0 0 0 0 0 0 0 0 ...
## $ GiniSimpson : num 0.817 0.57 0.92 0.819 0.521 ...
## $ Simpson : num 0.142 0.152 0.555 0.256 0.138 ...
## $ Shannon : num 0.67 0.512 0.863 0.695 0.471 ...
## $ Heip : num 0.291 0.22 0.693 0.385 0.19 ...
## $ McIntosh : num 0.658 0.428 0.852 0.688 0.384 ...
## $ SmithWilson : num 0.415 0.35 0.627 0.315 0.325 ...
## $ Pielou : num 0.19 0.194 0.36 0.245 0.178 ...3 Methods
Figure 3.1: Temperature timeseries figure
Figure 3.2: Temperature timeseries figure with real data
3.1 Variables estimated and modelled
(Perhaps make this into a table.)
Let \(N_{i,t,s}\) be the abundance (sometimes it was biomass data when abundance data were not available) of species \(i\) at time \(t\) at site \(s\). Total abundance at time \(t\) at site \(s\) is \(N_{t,s} = \sum_{i=1}^{s} N_{t,s,i}\).
Community stability at site \(s\) was estimated as the inverse of the coefficient of temporal variation in total community abundance (when abundance info were not available, then biomass): \(TempStab_s = 1 / CV(N_{t,s}) = abs(mean(N_{t,s})) / sd(N_{t,s})\)
Species richness at site \(s\) was estimated as the number of total species (\(nsp\)) and dominant species that were present minimum 70% of the total years sampled (\(R\)).
Species evenness at site \(s\) was estimated as Smith-Wilson matrix.
Community variance ratio: a measure of synchrony, scaled between 0 to 1 (Loreau & Mazancourt).
Community level total tail association from pairwise synchrony: see BioDyn project, Figure 1.
Temperature median: Median of CHELSA-extracted annual temperature timeseries for the study years included in the analysis for each community.
Temperature trend: Monotonic trend of annual temperature timeseries (computed by non-parametric Sen’s method or parametric linear fit slope). I used the Sen’s slope in the path model, as non-parametric estimation has some advantage, see wikipedia, but it is very similar to linear slope (see 4.16).
Temperature skew: Skewness of CHELSA-extracted annual temperature timeseries for the study years included in the analysis for each community.
Temperature variability: Temperature variability for the community during the study period = IQR(annual temperature distribution for the study period)/abs(median(annual temperature)). [Note: in Celcius scale temperature t_med could be negative for some sites, so use absolute value always]
4 Results
4.1 Community stability exploration
Figure 4.1: Stability-diversity relationship for birds and fish.
4.1.1 Birds
Figure 4.2: Stability-diversity relationship for birds at different temperature levels
Figure 4.3: Stability-temperature relationship for bird communities at different richness levels
Figure 4.4: Stability-synchrony relationship for birds at different temperature levels
Figure 4.5: Synchrony-temperature relationship (scatterplot)
Figure 4.6: Synchrony-temperature relationship (boxplot)
Figure 4.7: Synchrony richness relationship.
Figure 4.8: Synchrony temperature relationship.
4.1.1.1 Basic statistics for birds
Model of bird stability:
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 4.3009 | 0.4507 | 9.5429 | 0.0000 |
| nsp | 0.0315 | 0.0107 | 2.9469 | 0.0033 |
| t_med_celcius | -0.1413 | 0.0370 | -3.8197 | 0.0001 |
| nsp:t_med_celcius | 0.0034 | 0.0009 | 3.8206 | 0.0001 |
Model of bird synchrony:
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 0.2954 | 0.0218 | 13.5237 | 0.0000 |
| nsp | -0.0027 | 0.0005 | -5.2091 | 0.0000 |
| t_med_celcius | 0.0033 | 0.0018 | 1.8185 | 0.0692 |
| nsp:t_med_celcius | -0.0001 | 0.0000 | -1.4679 | 0.1424 |
4.1.1.2 Bird conclusions
Bird communities display a positive richness stability relationship. This relationship is stronger at higher temperatures. Equally, high richness bird communities are more stable at higher temperatures, while low richness bird communities are less stable at higher temperatures.
There is some suggestion that this may be explained by synchrony, but the statistics show no strong associations of synchrony with \(t_{med}\).
4.1.2 Fish
Figure 4.9: Stability-diversity relationship at different temperature levels
Figure 4.10: Stability-temperature relationship at different richness levels
Figure 4.11: Stability-synchrony relationship at different temperature levels
Figure 4.12: Synchrony-temperature relationship (scatterplot)
Figure 4.13: Synchrony-temperature relationship (boxplot)
Figure 4.14: Synchrony richness relationship.
Figure 4.15: Synchrony temperature relationship.
4.1.2.1 Fish basic statistics
Model of fish stability:
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 0.3925 | 0.1402 | 2.7986 | 0.0053 |
| log2(nsp) | 0.0567 | 0.0797 | 0.7109 | 0.4774 |
| t_med_celcius | 0.0270 | 0.0167 | 1.6152 | 0.1068 |
| log2(nsp):t_med_celcius | -0.0105 | 0.0078 | -1.3434 | 0.1797 |
Model of fish synchrony:
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | -0.1910 | 0.1212 | -1.5752 | 0.1158 |
| log2(nsp) | -0.3236 | 0.0689 | -4.6968 | 0.0000 |
| t_med_celcius | -0.0293 | 0.0144 | -2.0267 | 0.0432 |
| log2(nsp):t_med_celcius | 0.0075 | 0.0068 | 1.1036 | 0.2702 |
4.1.2.2 Fish conclusions
No significant interaction between richness and temperature for fish.
Figure 4.16: Distribution of temperature trend estimated by non-parametric Sen’s slope, and parametric linear fit slope. Colored points are significant Sen’s slope (green: birds, blue: fish).
##
## Freshwater Terrestrial
## 0.3344828 0.2471910
Figure 4.17: Histogram plot for trends, both taxa.
4.2 Explanations
So, from the exploratory plots we can see: at higher temperature positive stability-diversity relationship becomes stronger for birds but for fish it becomes weaker. Also fish becomes more asynchronous with increasing temperature. So, why does that happen? to find this we could explore how much the bird species and fish species are consistent to temperature change across all communities.
The cue is: if fish species are not much consistent in their response to warming and vary across sites, that means you cannot make a conclusion that they would become similar with changing temperature. On another note, bird species should be more consistent towards warming if their is no change in their synchrony level across communities. Another possibility could be with changing temperature you might loose some species (its not just number of individuals, it will selectively prefer few species with better fitness), and then the communities will be dominated by few species with similar traits (so increasing synchrony). we will test this below.
From the above plots, we can see birds are showing consistent response-distribution across all temperature change, i.e., in either end of temperature spectrum (low or high end). That’s why the synchrony level remains similar for birds. But for fish, warming increases the richness (addition of new species), and as fish species now become more variable in response to temperature sensitivity (trait-variation), they show more asynchrony compared to low temperature scenario where only few species exists (see smaller circle size on the map for lowT,<50%CI) and show similar traits (so more synchrony). Note: when I show this to Frank, he commented on how much robust is the pattern for fish at low T as there are only few species existed across 145 sites - so it also depends on how we considered the lowT-highT communities. I set beyond 50% CI of temperature range as low/high. Even if I decrease that to 30% CI, still very few species found in low T sites (15 sp across 203 sites: 80% >0, 20% <0 line).
To further explore this idea: we collected traits data for birds and fish species used in the analysis. For fish-traits, I will use body length measurements, for bird-traits I will use HWI (Hand-wing index). From below figures: at high T, birds have slightly less dispersal ability (lower HWI), but richness is more or less uniformly spread at either temperature range. For fish, at lowT, few large species exists with similar traits (remember the previous histogram plot 90-10) showing higher synchrony, as temperature increases addition of new small fishes in the community (maybe better environment for them to exist in that temperature rather than too cold water) makes them asynchronous with more trait variation (histogram plot 66-34).
When I showed this to Blake, he was not convinced by the idea to split the data into two: low/high based on t_med (to him this temperature difference is more on latitudinal differences as shown in the map), and same species can exist in both communities - so why changing t_med should change the synchrony level for fish? and getting different bodysize fish from low/high t_med (fewer big fish in lowT and many smaller fish in highT) is not explaining why big fish should be more synchronous - is it because of fewer species (richness) or because bigger fish abundance change needs more time - not on annual scale?
So, I thought to make a plot of how community-level average response traits (average of standardised correlation between species abundance with t_med timeseries across sites) changes with increasing temperature (t_med)? For fish, it should decrease with increasing t_med, whereas for birds it should be a flat relationship.
Possible explanation:
Figure 4.18: Response variation with temperature
Now, we will do a path analysis for a simplistic mixed effect model to see the environmental effects on community stability for both taxa.
## Length Class Mode
## 1 lmerMod S4
## 1 lmerMod S4
## 1 lmerMod S4
## 1 lmerMod S4
## 1 lmerMod S4
## data 57 data.frame list##
|
| | 0%
|
|======================= | 33%
|
|=============================================== | 67%
|
|======================================================================| 100%
##
## Structural Equation Model of psem_birds
##
## Call:
## VR ~ R + E + MedianT + VarT + TrendT + SkewT
## R ~ MedianT + VarT + TrendT
## E ~ R + MedianT + VarT + TrendT
## A ~ R + E + VR + MedianT + TrendT + SkewT
## stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + SkewT
##
## AIC
## 13974.305
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## A ~ VarT + ... coef 1179.623 0.5959 0.4403
## R ~ SkewT + ... coef 1238.736 0.0072 0.9326
## E ~ SkewT + ... coef 1239.471 3.1590 0.0758
##
## --
## Global goodness-of-fit:
##
## Chi-Squared = NA with P-value = NA and on 3 degrees of freedom
## Fisher's C = 6.941 with P-value = 0.326 and on 6 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value P.Value
## VR R -0.3119 0.0325 841.0562 91.2969 0.0000
## VR E -0.2136 0.0300 1062.6045 50.2902 0.0000
## VR MedianT 0.0130 0.0465 198.2582 0.0767 0.7822
## VR VarT -0.0177 0.0284 1012.4961 0.3846 0.5353
## VR TrendT -0.0296 0.0379 584.4032 0.6002 0.4388
## VR SkewT -0.0168 0.0312 948.4304 0.2873 0.5921
## R MedianT -0.1054 0.0532 649.3517 3.8844 0.0492
## R VarT -0.1142 0.0267 822.8100 18.2258 0.0000
## R TrendT -0.0004 0.0342 1231.4095 0.0002 0.9896
## E R -0.0770 0.0315 1233.4093 5.9583 0.0148
## E MedianT 0.1246 0.0567 489.4629 4.7691 0.0294
## E VarT 0.0189 0.0290 794.5467 0.4209 0.5167
## E TrendT 0.0846 0.0378 1188.9556 4.9779 0.0259
## A R 0.7475 0.0224 464.0606 1099.9131 0.0000
## A E 0.1588 0.0213 716.9356 54.8898 0.0000
## A VR 0.6043 0.0209 1188.2246 833.3884 0.0000
## A MedianT -0.0315 0.0244 140.0482 1.6356 0.2030
## A TrendT 0.0102 0.0237 260.7704 0.1807 0.6711
## A SkewT -0.0543 0.0209 447.0396 6.6445 0.0103
## stability R 0.1298 0.0319 1107.7539 16.3968 0.0001
## stability E -0.0499 0.0225 1087.6030 4.8824 0.0273
## stability VR -0.6934 0.0269 1225.9934 663.5605 0.0000
## stability A -0.1314 0.0275 1220.8706 22.8119 0.0000
## stability MedianT 0.0010 0.0369 230.4998 0.0007 0.9783
## stability VarT -0.0114 0.0207 1041.3349 0.3034 0.5819
## stability TrendT 0.0315 0.0277 618.9160 1.2805 0.2582
## stability SkewT 0.0114 0.0225 893.3895 0.2556 0.6133
## stability R:MedianT 0.0445 0.0231 766.1533 3.6810 0.0554
## Std.Estimate
## -0.3119 ***
## -0.2136 ***
## 0.0130
## -0.0177
## -0.0296
## -0.0168
## -0.1054 *
## -0.1142 ***
## -0.0004
## -0.0770 *
## 0.1246 *
## 0.0189
## 0.0846 *
## 0.7475 ***
## 0.1588 ***
## 0.6043 ***
## -0.0315
## 0.0102
## -0.0543 *
## 0.1298 ***
## -0.0499 *
## -0.6934 ***
## -0.1314 ***
## 0.0010
## -0.0114
## 0.0315
## 0.0114
## 0.0506
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method Marginal Conditional
## VR none 0.15 0.32
## R none 0.01 0.65
## E none 0.03 0.57
## A none 0.58 0.60
## stability none 0.57 0.65##
|
| | 0%
|
|======================= | 33%
|
|=============================================== | 67%
|
|======================================================================| 100%
##
## Structural Equation Model of psem_fish
##
## Call:
## VR ~ R + E + MedianT + VarT + TrendT + SkewT
## R ~ MedianT + VarT + TrendT
## E ~ R + MedianT + VarT + TrendT
## A ~ R + E + VR + MedianT + TrendT + SkewT
## stability ~ R + E + VR + A + (R:MedianT) + MedianT + VarT + TrendT + SkewT
##
## AIC
## 6184.980
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## A ~ VarT + ... coef 303.1369 0.3107 0.5777
## R ~ SkewT + ... coef 414.2328 3.7572 0.0533
## E ~ SkewT + ... coef 236.9543 1.0553 0.3053
##
## --
## Global goodness-of-fit:
##
## Chi-Squared = NA with P-value = NA and on 3 degrees of freedom
## Fisher's C = 9.335 with P-value = 0.156 and on 6 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value P.Value
## VR R -0.5500 0.0600 370.1560 81.8668 0.0000
## VR E -0.2934 0.0401 566.3523 52.9244 0.0000
## VR MedianT -0.2564 0.0598 128.1194 18.0395 0.0000
## VR VarT -0.0332 0.0393 572.6102 0.7037 0.4019
## VR TrendT 0.0680 0.0394 434.9108 2.9230 0.0880
## VR SkewT -0.0918 0.0495 193.1105 3.3642 0.0682
## R MedianT 0.1327 0.0521 208.9389 6.4142 0.0121
## R VarT -0.0045 0.0260 515.8896 0.0296 0.8636
## R TrendT -0.0099 0.0284 575.8529 0.1214 0.7276
## E R -0.4363 0.0607 452.1873 50.7083 0.0000
## E MedianT -0.1376 0.0628 143.6693 4.7304 0.0313
## E VarT -0.0272 0.0407 568.8198 0.4419 0.5065
## E TrendT 0.0440 0.0417 497.3481 1.1011 0.2945
## A R 1.0133 0.0323 59.1753 889.8806 0.0000
## A E 0.1100 0.0236 383.3190 21.1445 0.0000
## A VR 0.1107 0.0242 514.2745 20.6184 0.0000
## A MedianT -0.1029 0.0270 54.6353 13.9146 0.0005
## A TrendT 0.0247 0.0213 251.1697 1.3024 0.2549
## A SkewT -0.0046 0.0243 101.7171 0.0350 0.8521
## stability R -0.2936 0.1089 560.5680 7.2212 0.0074
## stability E -0.2117 0.0426 559.8101 24.5435 0.0000
## stability VR -0.5543 0.0418 554.7561 174.7950 0.0000
## stability A 0.1764 0.0684 540.3988 6.6299 0.0103
## stability MedianT -0.0227 0.0762 177.8652 0.0880 0.7671
## stability VarT 0.0258 0.0386 525.4657 0.4459 0.5046
## stability TrendT -0.0616 0.0413 562.8284 2.2049 0.1381
## stability SkewT -0.1847 0.0573 357.1907 10.2484 0.0015
## stability R:MedianT -0.0416 0.0633 568.5887 0.4311 0.5117
## Std.Estimate
## -0.5500 ***
## -0.2934 ***
## -0.2564 ***
## -0.0332
## 0.0680
## -0.0918
## 0.1327 *
## -0.0045
## -0.0099
## -0.4363 ***
## -0.1376 *
## -0.0272
## 0.0440
## 1.0133 ***
## 0.1100 ***
## 0.1107 ***
## -0.1029 ***
## 0.0247
## -0.0046
## -0.2936 **
## -0.2117 ***
## -0.5543 ***
## 0.1764 *
## -0.0227
## 0.0258
## -0.0616
## -0.1847 **
## -0.0358
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method Marginal Conditional
## VR none 0.39 0.49
## R none 0.04 0.53
## E none 0.25 0.42
## A none 0.78 0.78
## stability none 0.22 0.53
